Theta (4-12 Hz) and gamma (30-80 Hz) oscillations in the hippocampus are likely to be substrates for critical cognitive functions. To play such a role, the theta and gamma rhythms must be coherent across long distances (mm or more) in the brain. The mechanisms that lead to synchronization within and between local circuits separated by conduction delays are poorly understood. In the proposed work, two lab groups will collaborate to apply novel theoretical concepts of local and long-distance synchronization in electrophysiological experiments. Using the dynamic clamp technique, hippocampal microcircuits, containing biological and computationally simulated neurons that interact in real time, will be constructed. Together, the proposed theoretical and experimental studies will test the hypothesis that short- and long-range synchronization can be understood using the properties of mathematical symmetry and phase resetting properties of individual neurons and specific local neuronal microcircuits. We hypothesize that the phase resetting curves of the oscillatory neural modules contain all the information necessary to predict synchronization behavior, that synchronization between distal modules is based on symmetry between oscillators with similar frequencies, that in the presence of sufficiently strong coupling the symmetric mechanism is robust to biological levels of heterogeneity, and that harmonic locking between theta and gamma rhythms may play an important role in oscillatory coherence. Specific Aim 1. Test the hypothesis that synchronization of distal gamma modules mediated by long range excitatory connections results from near-symmetry (i.e., similar intrinsic frequencies and inter-module conduction delays) and preferential synchronization among similar distal modules. We will test theoretical predictions of synchronization based on phase resetting curves using gamma modules containing pyramidal cells and fast-spiking basket cell interneurons. Specific Aim 2. Test the hypothesis that N:1 locking between the gamma and theta rhythm aligns the firing of local oriens-lacunosum moleculare (O-LM) interneurons with that of a gamma cycle, with a fixed number of missed gamma cycles between theta cycles. Existence and stability conditions for N:1 locking based on the phase resetting curves will be used to predict when such locking occur. We will also determine whether N:1 locking can be sufficient to synchronize multiple O-LM interneurons within a local module, or if common external perturbations in the presence of such locking are required to promote theta coherence within local circuits. Predictions from phase-response measurements will be tested in hybrid microcircuits representing distant local circuits. Specific Aim 3. Test the hypothesis that synchronization of distal gamma modules mediated by O-LM interneurons firing at theta frequency also emerges as a consequence of near symmetry. In the case of synchronized O-LM cells, this extension is straightforward, but in practice, synchronization between O-LM cells is not required. We will test theoretical predictions of synchronization based on phase resetting curves using gamma modules connected via O-LM interneurons. Intellectual Merit: A novel approach to the highly significant question of how neural oscillators can synchronize their activity, particularly in the presence of conduction delays, is presented here. The theoretical and experimental aspects of the proposal are integrated in a synergistic way. Broader Impacts: There is a significant and highly interdisciplinary training component of this project at the undergraduate (B. Bullock, M. Woodman), graduate and postgraduate levels. With respect to diversity, at least one of the principal trainees will be an underrepresented minority and one principal investigator is female.